Dynamics Notes 1 Newton s Laws

Transcription

1 Dynamics Notes 1 Newton s Laws In 1665 Sir Isaac Newton formulated three laws that dictate the motion of objects. These three laws are universal and apply to all forces in the universe. Newton s 1 st Law: An object ample: and an object unless Newton s 2 nd Law: ample: As a formula: Newton s 3 rd Law: For every amples: As a formula: Free Body Diagrams: (Draw one for EVERY force question) 1) Represent the object 2) Represent all forces amples: Draw FBDs for each situation 1. A textbook sits motionless on a table. 2. A coconut falls from a tree (no air friction) 3. A puck slides along frictionless ice. 4. A dragster accelerates from rest. 5. A car drives at a constant velocity. 6. A block of wood slides down an incline

2 1. A student pulls straight upwards with a force of 650 N on their 15 kg backpack. What is the backpack s acceleration? 2. A 1200kg car accelerates at 5.85 m/s 2. If the force of friction acting on the car is 2800 N, how much force does the engine exert? Trickery Alert! Just when you though you were done with kinematics, they sneak back in. You will be expected to use kinematics to solve for acceleration to use in force problems and vice : A 2.10 kg curling rock is hurled down ice at 6.5 m/s. It comes to a stop in 12.0 s. What is the force of friction between the ice and the rock? Even More Trickery! Remember that when determining the forces working on an object we need to consider their directions. If a force is working in the direction of acceleration we need to break it down into components. : A boy pulls his 8.0 kg toboggan by a rope that angles 32 o above the horizontal. If his 36.0 kg sister sits on the toboggan, how much force does he need to exert to accelerate them at 2.25 m/s 2? (Assume no friction) NOTE:

3 Friction is created whenever Dynamics Notes 2 - Friction Force of friction (F f ) is given by the equation: On the microscopic level Where: F N = μ = = There are 2 types of friction: Static Friction: Note that the irregularities in a static object will tend to dig in more and generally: Kinetic Friction: Friction static μ s Friction kinetic μ k 1: A 3.75 kg block is pushed along a tabletop with a force of 45.0N. The coefficient of friction is a) Find the force of friction. b) Find its acceleration. 2: A kg puck is pushed along a sheet of ice with a force of N. If it moves at a constant velocity, find the coefficient of friction 3: A 1.12 kg textbook is pushed horizontally against a wall with a coefficient of friction of What is the least amount of force required to keep the book from slipping?

4 Two students push a crate across a frictionless surface. Student A pushes with 75 N East and Student B pushes with 48 N South. What is the resultant force acting on the box? Dynamics Notes 3 Forces in 2-D As with any vectors, forces must be resolved with consideration to both their and. If there are more than two forces then it is best to solve for the resultant using the... Resolve these force vectors into their x and y components F 1 = 35 N F 2 = 45 N F 3 = 65 N 20 o 2 - Determine the resultant force if all three forces in the last example are applied to a single body. F 3 F 1 F 2 3: Two children pull a third child on a toboggan (shown from the top, assume up is north). Assuming that they pull on ropes that are parallel to the ground determine the magnitude of the force exerted on the toboggan. F R

5 A ball sitting on a level surface will not roll because the forces on it are balanced (F net = 0). Dynamics Notes 4 Inclines However, when the ball is placed on an inclined plane it will roll down the plane. Although the F g pulls straight down at all times For inclined plane questions our first step should always be to resolve the object s F g into two components: F N is always Two important things to notice: 1) Only the pulls down the ramp. 2) The is equal and opposite to. An 8.0 kg block slides down the frictionless inclined plane shown. What is its acceleration? How much force is required to push an 11 kg block up the frictionless ramp shown at a constant velocity? A 15 kg block sits on an inclined ramp whose coefficient of friction is Find the block s acceleration. 35 o 58 o 40 o

6 Dynamics Notes 5 Two Objects and Tension There are a number of common force problems that involve 2 objects, that you will be expected to be able to solve. We will focus on 3 of these. 1) Atwood s Machine: Two masses suspended by a pulley Diagram: Include all forces at work on the two masses. Both masses have a F g that pull downwards, but since they are connected by a pulley those forces work in. The masses will accelerate so that the Since they are attached by a rope the acceleration of the masses must be. Note that there is a force of TENSION (T) that exists along the rope. Tension acts the same as all other forces, with two important peculiarities: 1) It is an internal force, acting 2) It cancels out The Strategies: When solving these problems it is easiest for us to choose the direction Remember that the acceleration on the two masses... It can also be easier to conceptualize this problem if we unfold the masses and lay them out in a line, while keeping all of our forces as they are I know that sounds weird so, here s an example. Two masses are suspended from a lightweight rope over a frictionless pulley as shown. What will their acceleration be once released? kg kg NOTE: When calculating the acceleration we use the because the F net is accelerating the entire system (both masses)!

7 Alright that wasn t too hard, but can you find the tension in the rope? If we use the same force diagrams and equations as before we hit a snag. The two tension forces!!! Strategy: To solve for tension chop your diagram in half and only consider one of the masses. Either one is fine because This is because tension is an. In order to solve for tension we have to consider - Find the tension in the rope in the preceding example. Note: When finding the tension we are only considering half of the equation therefore we only use. 2) Multiple Horizontal Masses: Attached by a cord Consider the masses shown. If µ = 0.25 for both blocks, find: a. the acceleration of the entire system b. the tension T in the rope between the blocks. T 8.0 kg 6.0 kg F = 75 N 3) The Hanging Mass: One mass hanging, one horizontal Consider the two masses shown. Find their acceleration and the tension in the rope. 8.0 kg 6.0 kg

8 Dynamic Notes 6 Two Objects and Inclines Because one tricky concept is never enough, I give you Two forces are attached by a rope over a frictionless pulley as shown. (Assume the incline is frictionless) Determine: a. The acceleration of the masses. b. The tension in the rope. m 1 = 4.0 kg 30 o m 2 = 6.0 kg Problem: What direction will they accelerate? In earlier pulley problems it was obvious, the bigger mass always wins. When an inclined plane is involved this is not always the case because for the mass on an incline only... So determine the forces on each one separately and see which one is the winner. Force 1 = Force 2 = In the name of physics, a monkey is attached to a sleeping sheep on a ramp. Don t ask why. As we all know, the coefficient of friction for a sleeping sheep on a ramp is precisely Determine: a. The acceleration of the system. b. The tension in the rope. even adorabler sheep 28 kg Strategies: 1. Find the forces acting on the two bodies separately to determine a winner 2. Determine the friction on the sheep. Friction can work either up or down the ramp, because it always opposes motion, so we don t know which direction it is acting until we know the winner. 3. Based on the winner find the acceleration using m total 4. Choose either body and examine it separately to determine the tension in the rope adorable monkey 24 kg 40 o